Theory of competitive solvation of polymers by two solvents and entropy-enthalpy compensation in the solvation free energy upon dilution with the second solvent

We develop a statistical mechanical lattice theory for polymer solvation by a pair of relatively low molar mass solvents that compete for binding to the polymer backbone. A theory for the equilibrium mixture of solvated polymer clusters {A(i)BC(j)} and free unassociated molecules A, B, and C is formulated in the spirit of Flory-Huggins mean-field approximation. This theoretical framework enables us to derive expressions for the boundaries for phase stability (spinodals) and other basic properties of these polymer solutions: the internal energy U, entropy S, specific heat C-V, extent of solvation Phi(solv), average degree of solvation < N-solv >, and second osmotic virial coefficient B-2 as functions of temperature and the composition of the mixture. Our theory predicts many new phenomena, but the current paper applies the theory to describe the entropy-enthalpy compensation in the free energy of polymer solvation, a phenomenon observed for many years without theoretical explanation and with significant relevance to liquid chromatography and other polymer separation methods. (C) 2015 AIP Publishing LLC.